reasoning

induction, problem of

Problem of justifying the inductive inference from the observed to the unobserved. It was given its classic formulation by David Hume, who noted that such inferences typically rely on the assumption that the future will resemble the past, or on the assumption that events of a certain type are necessarily connected, via a relation of causation, to events of another type. (1) If we were asked why we believe that the sun will rise tomorrow, we would say that in the past the Earth turned on its axis every 24 hours (more or less), and that there is a uniformity in nature that guarantees that such events always happen in the same way. But how do we know that nature is uniform in this sense? We might answer that, in the past, nature has always exhibited this kind of uniformity, and so it will continue to be uniform in the future. But this inference is justified only if we assume that the future must resemble the past. How do we justify this assumption? We might say that in the past, the future turned out to resemble the past, and so in the future, the future will again turn out to resemble the past. The inference is obviously circular: it succeeds only by tacitly assuming what it sets out to prove, namely that the future will resemble the past. (2) If we are asked why we believe we will feel heat when we approach a fire, we would say that fire causes heat—i.e., there is a “necessary connection” between fire and heat, such that whenever one occurs, the other must follow. But, Hume asks, what is this “necessary connection”? Do we observe it when we see the fire or feel the heat? If not, what evidence do we have that it exists? All we have is our observation, in the past, of a “constant conjunction” of instances of fire being followed by instances of heat. This observation does not show that, in the future, instances of fire will continue to be followed by instances of heat; to say that it does is to assume that the future must resemble the past. But if our observation is consistent with the possibility that fire may not be followed by heat in the future, then it cannot show that there is a necessary connection between the two that makes heat follow fire whenever fire occurs. Thus we are not justified in believing that (1) the sun will rise tomorrow or that (2) we will feel heat when we approach a fire. It is important to note that Hume did not deny that he or anyone else formed beliefs about the future on the basis of induction; he denied only that we could know with certainty that these beliefs are true. Philosophers have responded to the problem of induction in a variety of ways, though none has gained wide acceptance.

Method of raising the temperature of an electrically conductive material by subjecting it to an alternating electromagnetic field. Energy in the electric currents induced in the object is dissipated as heat. Induction heating is used in metalworking to heat metals for soldering, tempering, and annealing, and in induction furnaces for melting and processing metals. The principle of the induction-heating process resembles that of the transformer. A water-cooled coil (inductor), acting as the primary winding of a transformer, surrounds the material to be heated (the workpiece), which acts as the secondary winding. Alternating current flowing in the primary coil induces eddy currents in the workpiece, causing it to become heated. The depth to which the eddy currents penetrate, and therefore the distribution of heat within the object, depend on the frequency of the primary alternating current and the magnetic permeability, as well as the resistivity, of the material.

In logic, a type of nonvalid inference or argument in which the premises provide some reason for believing that the conclusion is true. Typical forms of inductive argument include reasoning from a part to a whole, from the particular to the general, and from a sample to an entire population. Induction is traditionally contrasted with deduction. Many of the problems of inductive logic, including what is known as the problem of induction, have been treated in studies of the methodology of the natural sciences. SeealsoJohn Stuart Mill; philosophy of science; scientific method.

Modification in the distribution of electric charge on one material under the influence of an electric charge on a nearby object. It occurs whenever any object is placed in an electric field. When a negatively charged object is brought near a neutral object, it induces a positive charge on the near side of the object and a negative charge on the far side. If the negative side of the original object is momentarily grounded, the negative charge may escape, so that the object becomes positively charged by induction.

In logic, a type of inference or argument that purports to be valid, where a valid argument is one whose conclusion must be true if its premises are true (seevalidity). Deduction is thus distinguished from induction, where there is no such presumption. Valid deductive arguments may have false premises, as demonstrated by the example: “All men are mortal; Cleopatra is a man; therefore, Cleopatra is mortal.” Invalid deductive arguments sometimes embody formal fallacies (i.e., errors of reasoning based on the structure of the propositions in the argument); an example is “affirming the consequent”: “If A then B; B; therefore, A” (seefallacy; formal and informal).

Reasoning is the cognitive process of looking for reasons for beliefs, conclusions, actions or feelings. Humans have the ability to engage in reasoning about their own reasoning using introspection. Different forms of such reflection on reasoning occur in different fields. Although reasoning was once thought to be a uniquely human capability, other animals also engage in reasoning.

In philosophy, the study of reasoning typically focuses on what makes reasoning efficient or inefficient, appropriate or inappropriate, good or bad. Philosophers do this by either examining the form or structure of the reasoning within arguments, or by considering the broader methods used to reach particular goals of reasoning. Psychologists and cognitive scientists, in contrast, tend to study how people reason, which cognitive and neural processes are engaged, how cultural factors affect the inferences people draw. The properties of logics which may be used to reason are studied in mathematical logic. The field of automated reasoning studies how reasoning may be modelled computationally. Laywers also study reasoning.

History of reasoning

It is likely that humans have used reasoning to work out what they should believe or do for a very long time indeed. However, some researchers have tried to determine when, in the history of human development, humans moved from using myths to describe the world to attempting to reason about the world, and when humans first began to reason about their own reasoning.

Babylonian reasoning

In Mesopotamia, Esagil-kin-apli's medical Diagnostic Handbook written in the 11th century BC was based on a logical set of axioms and assumptions, including the modern view that through the examination and inspection of the symptoms of a patient, it is possible to determine the patient's disease, its aetiology and future development, and the chances of the patient's recovery.

Greek reasoning

The works of Homer, written in the eighth century BC, contain mythic stories that use gods to explain the formation of the world. However, only two centuries later, late in the sixth century BC, Xenophanes of Colophon began to question the Homeric accounts of the creation of nature and the gods. He wrote:

“Homer and Hesiod attribute all things to the gods that among men are shame and a disgrace” (frag. 11).

“God is one, greatest among gods and among men, in no way like men in form and thought” (frag. 23).

“If oxen and horses and lions had hands or could paint and make things with their hands like men, then they would paint the forms of gods and make their bodies each according to their own shapes, horses like horses, oxen like oxen” (frag. 15).

According to David Furley, "the basis of [Xenophanes'] criticism appears to have been that he saw an inconsistency between the concept of god as something different from man, and the stories told about the gods, which made them behave as men do. In the same period, other Greek thinkers began to develop theories about the nature of the world that suggest that they believed that there were regularities in nature and that humans could use reasoning to develop a consistent story about the nature of the world. Thales of Miletus, c. 624 BC – c. 546 BC, proposed that all is water. Anaximenes of Miletus, c. 585 BC – c. 525 BC, claimed that air is the source of everything.

Aristotle is, so far as we know, the first writer to give an extended, systematic treatment of the methods of human reasoning. He identified two major methods of reasoning, analysis and synthesis. In the first, we try to understand an object by looking at its component parts. In the second, we try to understand a class of objects by looking at the common properties of each object in that class.

Aristotle developed what is known as syllogistic logic, which makes it possible to analyse reasoning in a way that ignores the content of the argument and focuses on the form or structure of the argument. In the Prior Analytics, Aristotle begins by pointing out that:

"[If] no pleasure is a good, neither will any good be a pleasure.

He then argues that this argument is an example of a rule of reasoning of the following form:

Premise: "Aristotle is Greek" and "All Greeks are human"

Conclusion: "Aristotle is Human"

Aristotle points out that by understanding the reasoning involved in this type of argument, we can know that whatever the As and Bs are, we can reach the same conclusion about the relationship between them. This is a simple and straightforward argument, but it is a sign of an amazing leap in understanding and research into reason and was the beginning of the development of formal logic.

Indian reasoning

Two of the six Indian schools of thought deal with logic: Nyaya and Vaisheshika. The Nyaya Sutras of Aksapada Gautama constitute the core texts of the Nyaya school, one of the six orthodox schools of Hindu philosophy. This realist school developed a rigid five-member schema of inference involving an initial premise, a reason, an example, an application and a conclusion. The idealistBuddhist philosophy became the chief opponent to the Naiyayikas. Nagarjuna, the founder of the Madhyamika "Middle Way" developed an analysis known as the "catuskoti" or tetralemma. This four-cornered argumentation systematically examined and rejected the affirmation of a proposition, its denial, the joint affirmation and denial, and finally, the rejection of its affirmation and denial. But it was with Dignaga and his successor Dharmakirti that Buddhist logic reached its height. Their analysis centered on the definition of necessary logical entailment, "vyapti", also known as invariable concomitance or pervasion. To this end a doctrine known as "apoha" or differentiation was developed. This involved what might be called inclusion and exclusion of defining properties. The difficulties involved in this enterprise, in part, stimulated the neo-scholastic school of Navya-Nyāya, which developed a formal analysis of inference in the 16th century.

Chinese reasoning

In China, a contemporary of Confucius, Mozi, "Master Mo", is credited with founding the Mohist school, whose canons dealt with issues relating to valid inference and the conditions of correct conclusions. In particular, one of the schools that grew out of Mohism, the Logicians, are credited by some scholars for their early investigation of formal logic. Unfortunately, due to the harsh rule of Legalism in the subsequent Qin Dynasty, this line of investigation disappeared in China until the introduction of Indian philosophy by Buddhists.

Islamic reasoning

For a time after Muhammad's death, Islamic law placed importance on formulating standards of argument, which gave rise to a novel approach to logic in Kalam, but this approach was later influenced by ideas from Greek philosophy and Hellenistic philosophy with the rise of the Mu'tazili philosophers, who highly valued Aristotle's Organon. The works of Hellenistic-influenced Islamic philosophers were crucial in the reception of Aristotelian logic in medieval Europe, along with the commentaries on the Organon by Averroes. The works of al-Farabi, Avicenna, al-Ghazali and other Muslim logicians who often criticized and corrected Aristotelian logic and introduced their own forms of logic, also played a central role in the subsequent development of medieval European logic.

Islamic logic not only included the study of formal patterns of inference and their validity but also elements of the philosophy of language and elements of epistemology and metaphysics. Due to disputes with Arabic grammarians, Islamic philosophers were very interested in working out the relationship between logic and language, and they devoted much discussion to the question of the subject matter and aims of logic in relation to reasoning and speech. In the area of formal logical analysis, they elaborated upon the theory of terms, propositions and syllogisms. They considered the syllogism to be the form to which all rational argumentation could be reduced, and they regarded syllogistic theory as the focal point of logic. Even poetics was considered as a syllogistic art in some fashion by many major Islamic logicians.

Reasoning methods and argumentation

One approach to the study of reasoning is to identify various forms of reasoning that may be used to support or justify conclusions. The main division between forms of reasoning that is made in philosophy is between deductive reasoning and inductive reasoning. Formal logic has been described as 'the science of deduction'. The study of inductive reasoning is generally carried out within the field known as informal logic or critical thinking.

Deductive reasoning

Deductive arguments are intended to have reasoning that is valid. Reasoning in an argument is valid if the argument's conclusion must be true when the premises (the reasons given to support that conclusion) are true. One classic example of deductive reasoning is that found in syllogisms like the following:

Premise 1: All humans are mortal.

Premise 2: Socrates is a human.

Conclusion: Socrates is mortal.

The reasoning in this argument is valid, because there is no way in which the premises, 1 and 2, could be true and the conclusion, 3, be false.

Validity is a property of the reasoning in the argument, not a property of the premises in the argument or the argument as a whole. In fact, the truth or falsity of the premises and the conclusion is irrelevant to the validity of the reasoning in the argument. The following argument, with a false premise and a false conclusion, is also valid, (it has the form of reasoning known as modus ponens).

Premise 1: If green is a colour, then grass poisons cows.

Premise 2: Green is a colour.

Conclusion: Grass poisons cows.

Again, if the premises in this argument were true, the reasoning is such that the conclusion would also have to be true.

In a deductive argument with valid reasoning the conclusion contains no more information than is contained in the premises. Therefore, deductive reasoning does not increase one's knowledge base, and so is said to be non-ampliative.

Inductive reasoning

Inductive reasoning contrasts strongly with deductive reasoning. Even in the best, or strongest, cases of inductive reasoning, the truth of the premises does not guarantee the truth of the conclusion. Instead, the conclusion of an inductive argument follows with some degree of probability. Relatedly, the conclusion of an inductive argument contains more information than is already contained in the premises. Thus, this method of reasoning is ampliative.

Abductive reasoning

Abductive reasoning, or argument to the best explanation, often involves both inductive and deductive arguments. However, as the conclusion in an abductive argument does not follow with certainty from its premises it is best thought of as a form of inductive reasoning. What separates abduction from the other forms of reasoning is an attempt to favor one conclusion above others, by attempting to falsify alternative explanations or by demonstrating the likelihood of the favored conclusion, given a set of more or less disputable assumptions.

Argument from analogy

Argument from analogy is usually also a form of inductive reasoning. An argument from analogy has the following form:

Reasoning by analogy goes from one particular thing, or category, to another particular thing, or category. As with other forms of inductive argument, even the best reasoning in an argument from analogy can only make the conclusion probable given the truth of the premises, not certain.

Fallacious reasoning

Formal fallacies

Formal fallacies occur when there is a problem with the form, or structure, of the argument. The word 'formal' refers to this link to the form of the argument. An argument that contains a formal fallacy will always be invalid. Consider, for example, the following argument:

#If a drink is made with boiling water, it will be hot.

#This drink was not made with boiling water.

#This drink is not hot.

The reasoning in this argument is bad, because the antecedent (first part) of the conditional (the 'if..., then...' statement) can be false without the consequent (second half) of the conditional being true. In this example, the drink could have been made with boiling milk, or heated in the microwave, and so be hot in spite of the truth of statement 2. This particular formal fallacy is known as denying the antecedent.

Informal fallacies

An informal fallacy is an error in reasoning that occurs due to a problem with the content, rather than mere structure, of the argument. Reasoning that commits an informal fallacy often occurs in an argument that is invalid, that is, contains a formal fallacy. One example of such reasoning is a red herring argument.

An argument can be valid, that is, contain no formal reasoning fallacies, and yet still contain an informal fallacy. The clearest examples of this occur when an argument contains circular reasoning, also known as begging the question.

Psychology

Scientific research into reasoning is carried out within the fields of psychology and cognitive science. Psychological research into reasoning falls into two general areas of research. First, the biological functioning of the brain is studied by neurophysiologists and neuropsychologists. Research in this area includes research into the structure and function of normally functioning brains, and of damaged or otherwise unusual brains. Second, psychologists carry out research on reasoning behaviour. Such research may focus, for example, on how people perform on tests of reasoning, such as intelligence or I.Q. tests, or on how well people's reasoning matches ideals set by logic (see, for example, the Wason test). In addition to carrying out research into reasoning, some psychologists, for example, clinical psychologists and psychotherapists work to alter people's reasoning habits when they are unhelpful.

In artificial intelligence, philosophers and scientists study reasoning and machines, and consider such questions as whether a machine can properly be considered to reason or think, and, relatedly, what would count as a test for reasoning. (See, for example, the Turing test.)

Legal reasoning

Legal reasoning is used when reflecting on the nature of existing laws or when reaching decisions about the relationship between laws and particular court cases.

Thorne McCarty did pioneering early work in the mechanization of legal reasoning for taxation using Micro Planner. More recent work on the formalization and mechanization of legal reasoning can be found in the proceedings of the International Conferences on Artificial Intelligence and Law ( most recently at Stanford in June 2007).